On the other hand, the research of many natural and social phenomena shows that the future development of many processes depends not only on their present state but also essentially on their historical information.
For example, the immune response of the vaccine of COVID-19 depends on the complete history of the vaccinator's exposure to microbial infection antigens; the quality of a harvest does not only depend on the current temperature of the environment, but also on the whole pattern of the past temperatures;
the price of the option depends not only on its current value but on the whole history of the underlying price, etc.
In the theory of stochastic processes, such phenomenons can be described by the stochastic differential delayed equations (SDDEs, for short). See Mohammed [1]}, [2]}, Chang [3]}, and the references therein.
